Fair division with minimal withheld information in social networks

Ivan Bliznets*, Anton Bukov, Danil Sagunov

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We present a study of a few graph-based problems motivated by fair allocation of resources in a social network. The central role in the paper is played by the following problem: What is the largest number of items we can allocate to the agents in the given social network so that each agent hides at most one item and overall at most k items are hidden, and no one envies its neighbors? We show that the problem admits an XP algorithm and is W[1]-hard parameterized by k. Moreover, within the running time, we can identify agents that should hide its items and can construct an ordering in which agents should pick items into its bundles to get a desired allocation. Besides this problem, we also consider the existence and verification versions of this problem. In the existence problem, we are given a social network, valuations, a budget, and the goal is to find an allocation without envy. In the verification problem, we are additionally given an allocation, and the goal is to determine if the allocation satisfies the required property.

Original languageEnglish
Article number114446
Number of pages16
JournalTheoretical Computer Science
Volume991
Early online date12-Feb-2024
DOIs
Publication statusPublished - 12-Apr-2024

Keywords

  • EF1 allocation
  • Fair division
  • Fixed-parameter tractable
  • FPT-algorithm

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